解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=42$$ 和公比：$$r=0.8571428571428571$$ 插入几何级数的公式：

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {0.8571428571428571}^{2-1}=42\cdot {0.8571428571428571}^1=42\cdot 0.8571428571428571=36$$

$$a_3=a_1·r^{n-1}=42\cdot {0.8571428571428571}^{3-1}=42\cdot {0.8571428571428571}^2=42\cdot 0.7346938775510203=30.857142857142854$$

$$a_4=a_1·r^{n-1}=42\cdot {0.8571428571428571}^{4-1}=42\cdot {0.8571428571428571}^3=42\cdot 0.629737609329446=26.448979591836732$$

$$a_5=a_1·r^{n-1}=42\cdot {0.8571428571428571}^{5-1}=42\cdot {0.8571428571428571}^4=42\cdot 0.5397750937109537=22.670553935860053$$

$$a_6=a_1·r^{n-1}=42\cdot {0.8571428571428571}^{6-1}=42\cdot {0.8571428571428571}^5=42\cdot 0.46266436603796024=19.43190337359433$$

$$a_7=a_1·r^{n-1}=42\cdot {0.8571428571428571}^{7-1}=42\cdot {0.8571428571428571}^6=42\cdot 0.3965694566039659=16.655917177366568$$

$$a_8=a_1·r^{n-1}=42\cdot {0.8571428571428571}^{8-1}=42\cdot {0.8571428571428571}^7=42\cdot 0.3399166770891136=14.276500437742772$$

$$a_9=a_1·r^{n-1}=42\cdot {0.8571428571428571}^{9-1}=42\cdot {0.8571428571428571}^8=42\cdot 0.2913571517906688=12.237000375208089$$

$$a_{10}=a_1·r^{n-1}=42\cdot {0.8571428571428571}^{10-1}=42\cdot {0.8571428571428571}^9=42\cdot 0.24973470153485897=10.488857464464077$$